It really depends on whom you ask. Personally, I believe yes.
If you look at the geography, it is likely that Chinese martial arts in the south traveled to Okinawa (a trading partner), from there to Japan, and then circling back to Korea from there. It is said that Fujian White Crane and Hung Gar are most likely the direct ancestors to Okinawan and Japanese karate, and you can certainly see the similarities.
The issue you have is that many Asian countries are very nationalistic (not necessarily a bad thing), and as such, disavow origins that would suggest a competing nation would be responsible for anything domestic. Even the word "Karate" itself used to translate to "Chinese Hand" (Tang Dynasty Hand), but it was later changed to mean "Empty Hand".
This is not to say that all martial arts in general have their origins in China; but you specifically ask about karate and kung fu.